Alter column, add default constraint

Try this

alter table TableName 
 add constraint df_ConstraintNAme 
 default getutcdate() for [Date]

example

create table bla (id int)

alter table bla add constraint dt_bla default 1 for id



insert bla default values

select * from bla

also make sure you name the default constraint..it will be a pain in the neck to drop it later because it will have one of those crazy system generated names...see also How To Name Default Constraints And How To Drop Default Constraint Without A Name In SQL Server

you can wrap reserved words in square brackets to avoid these kinds of errors:

dbo.TableName.[Date]